A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

Question

A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is (A) (MV2/T) (B) (1/2)(MV2/T2) (C) (MV2/T2) (D) (1/2)(MV2/T)

Tardigrade Admin · Accepted Answer

Power delivered in time T is P=F ⋅ V=M a V or P=M V (d V/d T) ⇒ P d T=M V d V ⇒ P T=(M V2/2) or P=(1 M V2/2) T

Q. A particle of mass $M$ , starting from rest, undergoes uniform acceleration. If the speed acquired in time $T$ is $V$ , the power delivered to the particle is

$\frac{M V ^{2}}{T}$

$\frac{1}{2} \frac{M V ^{2}}{T ^{2}}$

$\frac{M V ^{2}}{T ^{2}}$

$\frac{1}{2} \frac{M V ^{2}}{T}$

Power delivered in time $T$ is
$P = F \cdot V = M aV$
or $P = M V \frac{d V}{d T}$
$\Rightarrow P d T = M V d V$
$\Rightarrow PT = \frac{M V ^{2}}{2}$
or $P = \frac{1 M V ^{2}}{2} T$

Q. A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

TMV2​

21​T2MV2​

T2MV2​

21​TMV2​